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```Appendix

769

5. Efficiency of a Perfect Engine, that is, of an engine having a
reversible cycle. This is the highest efficiency to be obtained by
an engine working between given temperatures, and may therefore
be termed the ideal efficiency. It has already been shewn to be

where ra is the temperature of the furnace and r2 that of the
condenser. It includes, therefore, the efficiency of the boiler,
but, dealing only with the diagram horse power, does not take
account of mechanical imperfections. Supposing such efficiency
once obtained with given temperatures, the engine might yet be
improved by increasing the range of temperature, provided we
do not exceed the bounds of reason. Very often this efficiency
is taken for the engine only, with ^ as live steam temperature-;
but the steam being at a much lower temperature than the
furnace, a much lower ideal efficiency is possible. A very good
value by the first method is 77 per cent, and by the second, 32
per cent.

6. Thermal Efficiency of a Real Engine. — There are .two
methods of stating this, the relation of the work done to the heat
expended^ according to whether we include the boiler and engine,
or take the engine alone. Thus we have :

Thermal * efficiency (a) •«'**

33,000--772

Thermal  efficiency (b)

heat units in steam per I. H. P.
33,000-772

heat unjifs from coal per I. H. P.

Then a, good value for a might be 14 to 20 per cent., while
for b it might be 9 to 13 per cent Of course, if the thermal
efficiency is to be compared with the Carnot cycle, the latter
must be measured by similar temperatures. (See p. 883.)

7. Relative Efficiency.—This, as its name implies, is a com-
parison of the thermal efficiency of an engine with that of a
reversible cycle having the same range of temperature, and is the```